Yes Musescore is a good choice. If you get version 2+ you can produce guitar tablature. You can then save it as a .pdf file. It was originally a notation editor and I first produce notation and then get the tablature from that. It should be possible to write straight to tablature but you will have to learn the software. There is a very good online manual.

Basically, I intend to do a Youtube video based upon guitar arrangements of trad tunes. The approach to playing these tunes needs a bit of explanation, and so I want to back up the video with a written explanation and tabs. Presently, I just have the explanation written out on a word-processor, and hand-written tabs.

If you are using a word processor you may be able to simply "save as PDF" when you save the file. If you don't see "save as," you might also want to try selecting "Print," then in the options of sending to a printer or other form of software, it may also let you choose "Print to Adobe PDF" or another software that has a PDF printer (in looking at my printer choices I see Quicken also has one).

If you don't have this functionality in your word processor you may need to download a PDF maker. I haven't used Adobe Reader for a long time, but I'd start with Adobe and see if having that in your system allows you to save as PDF. (I can't test Reader for you because I have the full Adobe Acrobat software, and if I load Reader, it messes up my settings.)